QU1 Lecture Examples (Instructor: Kevin Strong)

Module 1

  1. Give the appropriate level of measurement for the following:

a)Test scores on a statistics exam

b)Jersey numbers of the Blue Bombers

c)High temperatures for the first 7 days in August in Winnipeg, MB

d)Supervisor’s performance ratings of excellent, very good, satisfactory, unsatisfactory, or very unsatisfactory

e)The distance that the students travel to this class

f)Social security numbers

g)Ranks of military personnel

  1. The city manager of Winnipeg is studying water usage. He selects a random sample of 30 families to determine the thousands of gallons used last year.

12, 23.7, 19.7, 15.4, 18.3, 23, 14.2, 20.8, 13.5, 20.7, 17.4, 18.6, 12.9, 20.3, 13.7, 21.4, 18.3, 29.8, 17.1, 18.9, 10.3, 26.1, 15.7, 14, 17.8, 33.8, 23.2, 12.9, 27.1, 16.6

a)Construct an array

b)Organize the data into a frequency distribution

c)Construct a histogram

d)Construct a less-than ogive

  1. The earnings per share of MTS common stock is below. Develop a simple line chart:

Year19881989199019911992

Earnings$4.433.954.724.753.01

  1. A sample of 212 college students was asked their favourite soft drink. Draw a pie chart.

Soft drink#

Coke78

Pepsi58

Dr. Pepper28

7-up24

Other24

Module 2

  1. A sample of 5 executives reported the following bonus last year (in $000’s): 14, 15, 17, 16, 15

a)Compute the sample mean

b)Assume it is a population, calculate the population mean

c)What is the mode? What is the median?

  1. The road life for a sample of 5 tires in thousands of miles is: 42, 51, 40, 39, 48. Compute the median.
  2. A sample of 6 employees had the following years of service: 16, 12, 8, 15, 7, 23. What is the median?
  3. Total enrolment at a large university increased from 18,246 in 1983 to 22,840 in 1992. Compute the geometric mean rate of increase over the period.
  4. During one hour on Friday, 50 soft drinks were sold at Wendy’s. Compute the weighted mean price of the soft drinks.

Price# Sold

$0.505

0.7515

0.9015

1.1015

  1. A sample of twenty stores revealed the following number of DVD players sold last weekend. Compute the mean, median and mode.

# soldFrequency

5-92

10-144

15-1910

20-243

25-291

a)Compute the mean

b)Compute the median

c)Compute the mode

  1. A sample of 5 accounting grads revealed the following starting salaries (in $000’s): 17, 26, 18, 20, 19.

a)Compute the range

b)Compute the mean average deviation

c)Compute the sample variance

d)Compute the standard deviation

e)Assume this is a population. Calculate the variance and standard deviation.

  1. A study of absentee records at Pollard Bank Note found the following number of days absent last year for a sample of 60 employees.

# days absentFrequency

1-33

4-616

7-924

10-1212

13-155

a)Compute the variance

b)Compute the standard deviation

c)Compute the coefficient of variation

Module 3

  1. Air Canada supplied the following information on their flights from Winnipeg to Toronto.

ArrivalFrequency

Early100

On time800

Late75

Cancelled25

a)What is the probability that a flight was on time?

b)What is the probability that a flight was early OR on time?

c)What is the probability that a flight was not cancelled?

  1. An investor owns two stocks: Nordic and MTS. Assume they are independent of each other. The probability that Nordic will increase next year is 0.50. The probability that MTS will increase next year is 0.70.

a)What is the probability that both stocks will increase in value next year?

b)What is the probability that at least one of the stocks will increase in value?

  1. The Dean of the Asper School of Business collected the following information about undergraduate students:

MajorMaleFemaleTotal

Accounting12080200

Finance11070180

Marketing7050120

Management110100210

Entrepreneur501060

HR14090230

Total6004001000

a)Compute the probability of selecting a female student at random

b)Compute the probability of selecting a male student or a management major

c)Given that the student is female, what is the probability that she is an accounting major?

  1. A woman has five dresses, four hats, and three pairs of shows. How many outfits does she have?
  2. A 3-character password on a computer must be 2 letters and a number in any order. How many codes are possible?
  3. A recent study found that 60% of mothers with kids under 10 are employed. Three are selected randomly.

a)What is the probability that they are all employed?

b)What is the probability that at least one of the mothers is employed?

  1. A loan manager has 10 loan applications. 8 are from previous homeowners and 2 are first time homebuyers. The manager selects 2 applications randomly. What is the probability that both of the applicants previously owned a home?
  2. The United Way has received funding applications from ten agencies.

a)If only three will be funded, how many different groups of three are possible?

b)If the United Way ranks the three agencies, how many arrangements are possible?

  1. Red Ketchup Company received a complaint that a bottle was not properly sealed. Based on the following information, what is the probability that the defect occurred at the Ross plant?

Plant% production% defective

Ross405

Spring308

Lake3010

  1. Enterprise reports the following number of cars rented per week over the past 20 weeks.

# cars rentedfrequency (# weeks)

105

116

127

132

a)Does this qualify as a probability distribution?

b)If not, convert it to a probability distribution.

c)Compute the expected (mean) number of cars rented per week.

d)Compute the variance and standard deviation of the number of cards rented per week.

  1. Stats Canada reports that 20% of the workforce in Selkirk is unemployed. A sample of 14 people is obtained. Compute the following probabilities:

a)3 are unemployed

b)3 or more are unemployed

c)At least one is unemployed

  1. An average of 13 cars pass through an intersection every 5 minutes. What is the probability that in the next 5 minutes, exactly 13 cars will pass through the intersection?

Module 4

  1. Daily water usage per person in Brandon is normally distributed with a mean of twenty litres and a standard deviation of 5 litres.

a)What percent of the population in Brandon uses less than 20 litres in a day? More than 20 litres?

b)What percent uses between 20 and 24 litres? Between 16 and 20 litres?

c)What percent uses more than 28 gallons?

d)What percent uses between 18 and 26 gallons?

e)Ten percent of the population uses how many gallons or more?

  1. A law firm has 5 partners, each reporting the number of hours they billed clients last week.

PartnerHours

Will22

Mack26

Yuri30

Steve26

Austin22

a)How many different samples of 2 can be chosen at random?

b)List all possible samples of size 2 and compute the mean (sampling distribution of the mean).

c)Organize the sample means into a frequency distribution and probability distribution.

d)Compute the mean of the sample means and compare it with the population mean.

e)Compute the standard error of the mean.

f)Compute the variance of the sampling distribution of the means.

Module 5

  1. A recent study showed that 15% of homes have a Tivo/PVR. A sample of 200 homes is obtained.

a)Of the 200 homes sampled, how many would you expect to have a Tivo (expected proportion = sample mean)? What is the variance?

b)What is the probability that less than 40 homes in the sample have Tivo?

c)What is the probability that exactly 40 homes have Tivo?

d)What is the probability that less than 25 homes have Tivo?

  1. At FedEx, the average weight of packages is 55 kg with a standard deviation of 20 kg. In a sample of 100 packages, what is the probability of getting a sample mean between 50 and 60 kg?
  2. The Dean of RRC wants to estimate the mean number of hours worked per week by students. A sample of 49 students showed a mean of 24 hours with a standard deviation of 4 hours.

a)Develop a 95% confidence interval for the mean number of hours worked per week if there are 10,000 students at RRC.

b)Does it make any difference if there are only 500 students at RRC?

c)Does it make any difference if the population size is not known?

d)Does it make any difference if the population size is unknown and the population variance is 16?

  1. A financial planner sampled 500 potential clients. 105 indicated that they planned to sell their home and retire to Arizona. Develop a 98% confidence interval for the proportion that plan to sell their home and retire to Arizona.
  2. A Pet Store wishes to estimate the proportion of kids that have a dog as a pet within 3% of the true population proportion with a 95% level of confidence, how many kids must they contact:

a)If they estimate that 50% have a dog as a pet.

b)If they estimate that 30% have a dog as a pet.

  1. A consumer group wants to estimate the mean monthly electric bill for a single family house in July. Based on similar studies, the standard deviation is estimated at $20. A 99% level of confidence is desired with an accuracy of plus or minus $5. How large a sample is required?
  2. Red Ketchup’s bottles should contain 16 ounces. The quality control department sampled and weighed 36 bottles and found a mean weight of 16.12 oz. with a standard deviation of 0.5 oz. At the 5% significance level, can we conclude that the process is out of control?

a)State the null and alternate hypotheses.

b)State the decision rule

c)Compute the test statistic from the sample data

d)What is the decision? Interpret the results.

e)What is the p-value?

  1. A manufacturer or flashlight batteries claims a life of 40 hours of use. The process is considered out of control if the mean of a sample of 36 batteries has a life of more than 42 hours and less than 38 hours. Assuming the population standard deviation is 6 hours:

a)What level of significance is implied?

b)What is the probability that a shift in the population mean to 39 hours will not be noticed (beta)?

c)What is the probability that a shift in the population mean to 37 hours will not be noticed?

Module 6

  1. EH Price used to produce 250 5-amp fuses per hour. A new machine is purchased that, according to the supplier, will increase the production rate. A sample of 10 randomly selected hours from last month revealed the mean hourly production of the new machine to be 256 per hour with a standard deviation of 6 per hour. At the 0.05 significance level, can they conclude that the new machine is faster? What is the p-value?
  2. In the past, 15% of the mail solicitations for United Way result in a contribution. A new letter has been drafted and is sent to a sample of 200 people and 45 respond with a contribution. At the 0.05 significance level, can it be concluded that the new letter is more effective? What is the p-value?
  3. A study was conducted to compare the mean number of years of service for those retiring in 1975 with those retiring last year. The following sample data was obtained. At the 0.01 significance level, can we conclude that the workers retiring last year had more years of service?

1975Last Year

Sample mean25.630.4

Population standard deviation2.93.6

Sample size4045

  1. A recent study compared fuel economy of domestic and import cars. A sample of 15 domestic cards had a mean of 33.7 miles per gallon and a standard deviation of 2.4. A sample of 12 imports had a mean of 35.7 mpg and a standard deviation of 3.9. At the 5% significance level can we conclude that the miles per gallon (fuel economy) are higher on the imported cars?
  2. An independent consumer group is comparing the daily rental cost of a compact car from Hertz and Avis. A random sample of 8 cities is obtained (see below). At the 5% significance level, can they conclude that there is a difference in the rental charge? What is the p-value?

CityHertzAvis

Atlanta$42$40

Chicago5652

Cleveland4543

Denver4848

Honolulu3732

Kansas4548

Miami4139

Seattle4650

  1. Are unmarried workers more likely to be absent from work than married workers? A sample of 250 married workers showed 22 missed more than 5 days last year, while a sample of 300 unmarried workers showed 35. Use the 0.05 significance level. What is the p-value?

Module 7

  1. A sample of 8 textbooks is chosen to study the relationship between the number of pages and cost.

BookPagesPrice

1500$28

270025

380033

460024

540023

650027

760021

880031

a)Plot a scatter diagram.

b)Compute the slope and y-intercept. What is the regression equation?

c)Compute the coefficient of correlation.

d)Test the hypothesis that there is no correlation in the population. α = 0.05

e)Test for significance of the slope. α = 0.05

  1. 10 students will graduate from the CGA program this quarter. The President asks 2 instructors to rank the students for scholarships. Given r = 0.73, n=10 and α = 0.05, can the president conclude that there is a positive association in the rankings of the 2 instructors?

StudentInstructor 1Instructor 2

124

235

352

486

541

6108

779

8910

913

1067

  1. For y = delivery time in minutes and x = distance in miles from the pizza shop, the least-squares regression line fitted to 62 observations yields the equation y = 16.9 + 1.225x. SST is 594 and SSE is 540.

a)Construct an ANOVA table

b)Find the standard error of the slope by assuming that SSx = 36. Use this to do a t-test to determine if the slope is significant.

c)Test the same relationship as in b), but use an F-test. Are the answers to b) & c) consistent?

d)Assuming normality, test whether there is a significant correlation between the distance and time. Compare this to b) & c).

  1. Fill in the blanks:

Regression Statistics

Multiple R

R squared

Adjusted R squared0.9868

Standard Error

Observations14

ANOVAdfSSMSF

Regression121528.6429

Residual (Error)

Total21794.8571

CoefficientStd. Errort StatP-value

Intercept12.67863.38950.0028

Lot Size1.96070.06290.0000

Module 8

  1. Shown below is the price per share and quantities owned at the end of 1988 and 1992 for 3 stocks you owned. Use 1988 as the base period.

Stock1988 Price1988 # shares1992 Price1992 # shares

Investors130250

Great-West515430

CanWest640620

a)Compute a simple price index for each stock

b)Compute a simple aggregate price index for the three stocks

c)Compute the price index using the Laspeyres method

d)Compute the price index using the Paasche method

e)Develop a value index

  1. The average disposable income increased from $79 in 1963 to $281 in 1983. During the same period, the CPI increased from 91.7 to 298.4 with a base year of 1967. Determine the real change in workers income in 1967 constant dollars.

Module 9

  1. A company is considering expanding its sales into a new area. Setup cost is $2,000. Sales price is $2.50 per unit. Manufacturing and distribution cost is $0.40 per unit. The projected sales levels and their associated probabilities of occurrence are:

Projected SalesProbability

40000.1

30000.4

20000.3

10000.2

a)Construct a payoff table

b)Determine the expected monetary value (EMV) for each alternative

c)Construct an opportunity loss table

d)Determine the expected opportunity loss (EOL) for each alternative

e)Compute the expected value of perfect information (EVPI)